Lie Symmetry Reductions and Exact Solutions of a Multidimensional Double Dispersion Equation

Abstract

In this paper, based on classical Lie group method, we study a multidimensional double dispersion equation, and get its infinitesimal generator, symmetry group and similarity reductions. In particular, similarity solutions and travelling wave solutions of the multidimensional double dispersion equation are derived from the reduction equations.

Conservation Laws and Travelling Wave Solutions for Double Dispersion Equations in (1+1) and (2+1) Dimensions

“…In [6], the authors have studied a multidimensional double dispersion equation u tt − ∆u − ∆u tt + ∆ 2 u + k∆u t = ∆f (u), x ∈ R n , t > 0, (1.1) with…”

Lie Symmetry Analysis, Optimal Systems and Explicit Solutions of the Dispersive Long Wave Equations

“…generalized simple equation method [21], generalized Tanh function method [22], homotopy perturbation method [23] and power series method [24], etc.) are effectively combined to reflect the complementarity of each other, which makes it possible to obtain exact solutions of some NLPDEs with physical significance, and attracts the attention and research of many scholars [25] [26] [27].…”